5 電容 Capacitance National Ignition Facility. Explosions in Airborne Dust

5 電容 Capacitance

National Ignition Facility

Explosions in Airborne Dust

5-1 電容與電容器

• 電容（ Capacitance ） • 平行板電容器 • C = ( F 法拉 ) K: 介電常數，真空 = 1 0: 真空電容率 A: 板面積 d : 兩板距

離

電位差電荷

V

qC

d

K 0

The Uses of Capacitors

As storehouses of electric potential energy

As vital elements in tuned circuits (radio and TV) and RAM chips

Charging a capacitor

5-2 Calculating the Capacitance

1) Put a charge q on the plates

2) Find E using Gauss’s Law

3) Find V between the plates

4) Calculate C by its definition

Calculating the electric field

EAqqAdE 00

Calculating the potential difference

)( VVVEdsV

sdEVV

if

f

iif

A parallel-plate capacitor

d

A

V

qC

EddsEEdsV

EAqd

0

0

0

A cylindrical capacitor

)/ln(

2or

)/ln(2

)ln(2

2

2

)2(

00

0

0

0

00

abL

C

ab

LC

a

b

L

q

r

dr

L

qEdsV

Lr

qE

rLEEAq

b

a

A spherical capacitor

4

4)

11(

4

4

4

1

)4(

0

00

20

20

200

ab

ab

V

qC

ab

abq

ba

q

r

drqEdsV

r

qE

rEEAq

b

a

An Isolated Sphere – the missing plate is a conducting sphere of infinite radius

)(b 4/1

4 00

Rba

aC

Ex.1 1.0 F 電容器

• d = 1.0mm

228

12

3

0

100~101.1

/1085.8

100.10.1

kmm

mF

mFCdA

Ex.2 a hyperbaric chamber

• Spark ： > 2000V

• fire ： > 0.20 mJ→

• Vf ： > 6000V

• Uf ： > 0.45 mJ

2 = , 1/ 2i i f fq CV C V U CV

Conducting floor

Ex.3 the threshold value Ut ( 150 mJ) required to ignite airborne grains.

20

3

0 0

4

4 , 1/ 2

2 2(150 10 )

4 4 (1.8m)

3.9 10 V

t

C R U CV

UV

R

5-3 Capacitors in parallel

等效電容

n

jjeq

eq

CC

CCCV

qC

VCCCqqqq

VCqVCqVCq

1

321

321321

332211

)(

, ,

5-4 Capacitors in series

等效電容

321

321

321321

33

22

11

1111

/1/1/1

1

)111

(

, ,

CCCC

CCCV

qC

CCCqVVVV

C

qV

C

qV

C

qV

eq

eq

Ex.4 Finding eq. capacitor

CVVVCq

qqC

qVVCq

CCCCCC

0.31)(

)( =

111 ,

121111

1231212

1212123123

3121232112

5-5 Storing Energy in an Electric Field

22

2

0

2

1

2

2

1

CVC

qU

C

qqdq

CdWW

qdC

qqdVdW

q

Ex.4 A RAM Chip

electrons108.1

1060.1

3.51055 619

15

C

VF

e

CV

e

qn

C = 55fF （ 10-15 ） V = 5.3 volt

Ex.5 電容式鍵盤

Ex.5 (cont)

• A = 9.50 10-5m2 ; k = 3.50 • 按鍵後 d 由 5.00mm 減為 0.150mm

• 按鍵前 C = 0.589PF

PFC 0.19

FPFd

k 120 106.19

電容式麥克風

Ex.6 defibrillator ( 除纖顫機 )

kW100s100.2

J200

J875)V5000)(F1070(2

1

2

1

3

262

t

UP

CVU

心跳停止病人之急救

1. 盡快求助2. 盡快給予先進的救命治療3. 盡快實行心肺復甦術

(CPR) 4. 盡快除纖顫